The accuracy of a measure (an approximate number) refers to the ratio of the size of the maximum possible error to the size of the number. This ratio is called the relative error. We express the accuracy as a percent, by converting the relative error to a decimal and subtracting it from 1 (and writing the resulting decimal as a percent). The smaller the relative error, the more accurate the measure.

The compensatory principle states that the smaller the unit used to measure the distance, the more of those units that will be needed. For example measuring a distance in centimeters will result in a larger number of that unit than measuring a distance in kilometers.

An irrational number is a number that cannot be written in the form a/b where both a and b are integers and b is not equal to 0. Informally, we often state that an irrational number has decimal places that continue infinitely without repeating.

Partitioning is the division of something into parts. In measurement, partitioning is done with units: A meter is divided into centimeters, a gallon is divided into quarts, and so on. The level of partitioning used in a measurement affects the precision of that measurement. For example, a measurement taken with a meter stick divided into centimeters is more precise than a measurement taken with an unmarked meter stick.

Pi () is the ratio between the circumference and diameter of a circle. Pi is a constant number, approximately 3.14159, and is irrational. The numbers 22/7 and 3.14 are frequently used as approximations to .

A polygon is a two-dimensional geometric figure with these characteristics: It is made of straight line segments; each segment touches exactly two other segments, one at each of its endpoints; and it is closed -- in other words it divides the plane into two distinct regions, one inside and the other outside the polygon.

The prefixes used by the metric system indicate the powers of 10 used to convert from one unit type to another. Common prefixes include "kilo-" for 1,000, "centi-" for one 100th, and "milli-" for one 1,000th.

A ratio is a comparison between two quantities. A measurement is a type of ratio -- it is a comparison with a unit. When we state that an object is eight inches long, we mean in comparison to the unit of one inch.

Referents make measurement tasks easier by establishing benchmarks for a certain measure. Two examples of referents are a stretch of road that is about a mile and an adult arm length that is about a meter.

The scale used on a map or model is an example of a measurement ratio. A map with a scale of 1:250 indicates that one unit on the map is equal to 250 units in the actual distances represented by the map.

Transitivity is a mathematical property stating that if A and B satisfy a relation and B and C satisfy the same relation, then A and C also satisfy the relation. Common examples include equality comparisons (if A = B and B = C, then A = C), inequality comparisons (if A < B and B < C, then A < C), and parallelism (if Line A is parallel to Line B, and Line B is parallel to Line C, then Line A is parallel to Line C). Transitivity allows objects to be compared indirectly, and allows measurements to be consistent in comparisons.

The U.S. customary system is the system of measurement typically used in the United States. Its units include inches, gallons, and pounds. This system is not as consistent as the metric system. Additionally, conversions between units are nonstandard -- how many people know how many drams are in a pennyweight?!

Weight is the force of gravity on an object. An object in a gravitational field has both a mass and a weight, which are not the same thing. For example, an object in outer space might be weightless, but it still has mass.